Polynomial matrices are particular cases of rational matrices. Therefore, the definitions above can be applied to polynomial matrices. However, standard literature on polynomial matrices [1]}, [2]} use the term eigenvalues instead of zeros and poles and define the structure at infinity in a different way. We discuss these points in this remark. Note first that a polynomial matrix \(P(\lambda )\)  does not have finite poles, i.e., all the indices \(d_i\)  in (REF ) are nonnegative for any finite \(\lambda _0\) . The finite eigenvalues of \(P(\lambda )\)  and their partial multiplicities [2]} are exactly the same as the finite zeros of \(P(\lambda )\)  and their partial multiplicities. However, in [2]}, a polynomial matrix \(P(\lambda )\)  of degree \(d\)  and normal rank \(r\)  is said to have an eigenvalue at infinity with partial multiplicities \(0 < t_p \le \cdots \le t_r\)  if the reversal polynomial matrix \(\text{rev}_d P(\lambda ) := \lambda ^d P(1/\lambda )\)  has an eigenvalue at 0 with partial multiplicities \(0 < t_p \le \cdots \le t_r\) . In this situation the structural indices (REF ) of \(P(\lambda )\)  at infinity when viewed as a rational matrix are
\( (d_{1}, d_{2},\ldots , d_{r})=(\underbrace{0,\ldots ,0}_{p-1}, t_p ,\ldots , t_r) - (d,d,\ldots , d).\) 
